Hidden Grassmann Structure in the XXZ Model IV: CFT Limit

Abstract

Abstract. The Grassmann structure of the critical XXZ spin chain is studied in the limit to conformal field theory. A new description of Virasoro Verma modules is proposed in terms of Zamolodchikov's integrals of motion and two families of fermionic creation operators. The exact relation to the usual Virasoro description is found up to level 6.

Quantum transfer-matrices for the sausage model

“…The constant γ is an arbitrary number belonging to the open segment 0 < γ < π 2 . We also swap p 2 for 95) and the kernels read explicitly as…”

“…Based on the results of these papers, we derived non-linear integral equations for determining the vacuum eigenvalues of the chiral transfermatrix which work both for the cigar and the parafermionic regimes. We believe that this might be a good starting point for applying the powerful fermionic methods [92][93][94][95][96] to the sausage/O(3) NLSM.…”

Exercises with the universalR-matrix

“…The Q-operator method has many applications in the theory of quantum integrable systems. We would like to mention here its important role in the recent investigation of the correlation functions of the XXZ-spin chain [10,11,24,9]. It is worth noting that, in general, for a given integrable system one has a set of transfer matrices and Q-operators which satisfy a whole system of functional relations.…”

Exact finite volume expectation values of $$ \overline{\varPsi}\varPsi $$ in the massive Thirring model from light-cone lattice correlators

“…Beyond our approach, there is another approach to the form-factors of the SG model in cylindrical geometry [65][66][67][68][69][70][71]. We close the paper with some discussion concerning the comparison of our method with that of the series of papers [65][66][67][68][69][70][71].…”

“…We close the paper with some discussion concerning the comparison of our method with that of the series of papers [65][66][67][68][69][70][71]. In [65][66][67][68][69][70][71] the hidden Grassmannian structure of the XXZ model was exploited to determine the finite temperature 1-point functions [70] and ratios of infinite volume form-factors [71] of the local operators of the SG theory. In this approach the compactified direction is time and the compactification length corresponds to the inverse temperature.…”